玻色子计算的物理普适模型与Solovay-Kitaev定理
A physical and universal model of bosonic computations with Solovay-Kitaev theorem
- Paderborn University（帕德博恩大学）
- PhoQS（光子量子系统中心）
- University of Toronto（多伦多大学）
- DIENS, École Normale Supérieure, PSL University, CNRS, INRIA（法国高等师范学院，巴黎文理研究大学，法国国家科学研究中心，法国国家信息与自动化研究所）
- Tufts University（塔夫茨大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对现有玻色子计算模型能量无界导致非物理的问题，提出能量保持的BEQC模型，证明其普适性并给出Solovay-Kitaev定理，应用于GKP态、Fock态制备及量子比特酉模拟。
AI中文摘要：
玻色子量子系统是量子信息处理的主要架构之一，提供具有强纠错能力的连续变量自由度。然而，标准的玻色子量子计算模型，如Lloyd-Braunstein模型[Lloyd和Braunstein，1999]和混合振子-量子比特模型[Brenner，Dias和Koenig，2025；Liu等人，2026]，允许能量急剧增长，导致非物理的计算能力，并破坏通用高效编译等基本算法工具[Brenner等人，2026；Rudolph等人，2025]。为解决这一问题，我们引入了一种新的玻色子量子计算模型——玻色子能量保持量子计算（BEQC），其中能量被视为一种计算资源。即，能量仅通过输入相干态提供，所有门由能量保持哈密顿量生成。因此，通过构造，能量急剧增长是不可能的，使模型具有物理基础。接下来，我们证明BEQC在许多方面是计算鲁棒且普适的，包括：（1.计算能力）BEQC高效模拟现有模型中所有多项式能量计算，并在多项式能量设置下精确恢复BQP。当改变模型的能量、精度和空间参数时，它进一步承认若干复杂性理论上界。（2.通用门集和态合成）BEQC具有基于线性光学和Kerr相互作用的自然通用门集。特别是，我们获得了绕过了先前不可能性结果的Solovay-Kitaev定理。我们给出了各种应用，包括（a）具有严格制备保证的GKP态工程协议，（b）Fock态制备达到指数精度，以及（c）对任何基于量子比特的酉变换进行原生Fock空间模拟。
英文摘要：
Bosonic quantum systems are among the leading architectures for quantum information processing, offering continuous-variable degrees of freedom with strong error-correction capabilities. However, standard bosonic quantum computation models such as the Lloyd-Braunstein [Lloyd and Braunstein, 1999] and hybrid oscillator-qubit models [Brenner, Dias, and Koenig, 2025; Liu et al., 2026] permit dramatic energy growth, leading to unphysical computational power and the breakdown of fundamental algorithmic tools such as universal and efficient compilation [Brenner et al., 2026; Rudolph et al., 2025]. To address this, we introduce a new model of bosonic quantum computation, Bosonic Energy-Preserving Quantum Computation (BEQC), in which energy is treated as a computational resource. Namely, energy is supplied solely through input coherent states, and all gates are generated by energy-preserving Hamiltonians. Thus, by construction, dramatic energy growth is impossible, making the model physically grounded. We next show that BEQC is a computationally robust and universal model in many respects, including: (1. Computational power) BEQC efficiently simulates all polynomial-energy computations in existing models, and exactly recovers BQP in the polynomial energy setting. It further admits several complexity-theoretic upper bounds when varying the energy, precision, and space parameters of the model. (2. Universal gate sets and state synthesis) BEQC has natural universal gate sets based on linear optics and Kerr interactions. In particular, we obtain a Solovay-Kitaev theorem which circumvents previous no-go results. We give various applications, including (a) a protocol for engineering GKP states with rigorous preparation guarantees, (b) Fock state preparation to exponential precision, and (c) native Fock space simulation of any qubit-based unitary.
